Spectral compression: Weighted principal component analysis versus weighted least squares

Two weighted compression schemes, Weighted Least Squares (wLS) and Weighted Principal Component Analysis (wPCA), are compared by considering their performance in minimizing both spectral and colorimetric errors of reconstructed reflectance spectra. A comparison is also made among seven different weighting functions incorporated into ordinary PCA/LS to give selectively more importance to the wavelengths that correspond to higher sensitivity in the human visual system. Weighted compression is performed on reflectance spectra of 3219 colored samples (including Munsell and NCS data) and spectral and colorimetric errors are calculated in terms of CIEDE2000 and root mean square errors. The results obtained indicate that wLS outperforms wPCA in weighted compression with more than three basis vectors. Weighting functions based on the diagonal of Cohen’s R matrix lead to the best reproduction of color information under both A and D65 illuminants particularly when using a low number of basis vectors.